Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts

Table 3

Comparisons of RME values of the proposed PSO optimized DIs with other integer order existing integrators optimized by different optimization techniques.

𝜔  (𝜋 rad)	Al-Alaoui 3-segment (SA)	Al-Alaoui 4-segment (SA)	Jain-Gupta-Jain (GA)	Upadhyay (P-Z)	Gupta-Jain-Kumar (LP)	Proposed 2nd order DI (PSO)	Proposed 3rd order DI (PSO)
0.25	−72.03	−60.18	−54.46	−48.31	−71.06	−72.03	−63.82
0.5	−49.15	−41.21	−59.47	−51.65	−59.89	−59.68	−73.04
0.75	−37.25	−34.02	−80.04	−61.71	−63.91	−53.27	−71.45
1.0	−30.29	−30.34	−57.28	−57.28	−49.94	−49.88	−64.63
1.25	−22.72	−32.96	−53.84	−48.71	−39.33	−48.71	−68.2
1.75	−11.64	−35.05	−53.85	−47.91	−31.46	−62.62	−54.2
2.0	−8.24	−19.11	−60.53	−52.89	−31.43	−49.98	−49.94
2.25	−6.92	−15.99	−53.84	−61.5	−34.5	−42.77	−53.66
2.75	−18.19	−19.73	−37.54	−37.76	−45.88	−55.55	−40.61
3.0	−4.17	−18.11	−35.52	−36.44	−30.14	−41.34	−45.01